Simplify the following expression: $p = \dfrac{-10x^2 + 20x + 800}{x - 10} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ p =\dfrac{-10(x^2 - 2x - 80)}{x - 10} $ Then we factor the remaining polynomial: $x^2 {-2}x {-80} $ ${-10} + {8} = {-2}$ ${-10} \times {8} = {-80}$ $ (x {-10}) (x + {8}) $ This gives us a factored expression: $\dfrac{-10(x {-10}) (x + {8})}{x - 10}$ We can divide the numerator and denominator by $(x + 10)$ on condition that $x \neq 10$ Therefore $p = -10(x + 8); x \neq 10$